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arXiv · 2206.03561

Stability of a new generalized reciprocal type functional equation

Idir Sadani
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Abstract

In this paper, we investigate the generalized Hyers-Ulam stability of the following reciprocal type functional equation \begin{equation*}f(2x+y)+f(2x-y)=\frac{2f(x)f(y)\displaystyle{\sum_{\substack{k=0\\ \text{$k$ is even}}}^{ l}2^{l-k}\binom{l}{k}f(x)^{\frac{k}{l}}f(y)^{\frac{l-k}{l}}}}{\left(4f(y)^{\frac{2}{l}}-f(x)^{\frac{2}{l}}\right)^l}\end{equation*} in non-zero real and non-Archimedean spaces.

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Idir Sadani. 2022-05-05. Stability of a new generalized reciprocal type functional equation. https://arxiv.org/abs/2206.03561

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